摘要
本文研究了具有转移条件且边界条件有特征参数的Sturm-Liouville算子T.首先由算子T本身出发研究其特征值问题,得到了λ是该边值问题的特征值的充要条件.借助新空间H和新算子A,通过构造算子A的Green函数,证明了算子T的特征函数扩张成新算子A的特征函数形成H的标准正交基.
In this paper, we investigate the Sturm-Liouville operators with transmission conditions and eigenparameter-dependent boundary conditions. By means of studying the operator itself, we study properties of its eigenvalues, and obtain the necessary and sufficient conditions for λ is an eigenvalue. By constructing the Green＇s function of the new operator A, we prove the completeness of their eignfunctions.
出处
《应用数学学报》
CSCD
北大核心
2012年第1期156-167,共12页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(10861008
11161030)资助项目
